Existing causal methods for time-varying exposure and time-varying confounding focus on estimating the average causal effect of a time-varying binary treatment on an end-of-study outcome. Methods for estimating the effects of a time-varying continuous exposure at any dose level on the outcome are limited. We introduce a scalable, non-parametric Bayesian framework for estimating longitudinal causal dose-response relationships with repeated measures.We incorporate the generalized propensity score either as a covariate or through inverse-probability weighting, formulating two Bayesian dose-response estimators. The proposed approach embeds a double non-parametric generalized Bayesian bootstrap which enables a flexible Dirichlet process specification within a generalized estimating equations structure, capturing temporal correlation while making minimal assumptions about the functional form of the continuous exposure. We applied our proposed approach to a motivating study of monthly metro-ridership data and COVID-19 case counts from major international cities, identifying causal relationships and the dynamic dose-response patterns between higher ridership and increased case counts.

翻译：现有针对时变暴露与时变混杂因素的因果推断方法主要关注时变二元处理对研究终点结局的平均因果效应估计。对于时变连续暴露在任意剂量水平对结局影响的估计方法仍较为有限。本文提出一种可扩展的非参数贝叶斯框架，用于估计具有重复测量数据的纵向因果剂量-反应关系。我们通过将广义倾向评分作为协变量或采用逆概率加权方式，构建了两种贝叶斯剂量-反应估计量。该方法嵌入了双重非参数广义贝叶斯自助法，可在广义估计方程框架内实现灵活的狄利克雷过程设定，从而在捕获时间相关性的同时对连续暴露的函数形式做出最小化假设。我们将所提方法应用于一项实证研究，该研究分析了多个国际大都市的月度地铁客流量数据与COVID-19病例数，成功识别了更高客流量与病例增长之间的因果关系及动态剂量-反应模式。